Background The Covid-19 pandemic is one of the most serious global public health threats in recent times. Understanding transmission of SARS-CoV-2 is of utmost importance to be able to respond to outbreaks and take action against spread of the disease. Transmission within the household is a concern, especially because infection control is difficult to apply within the household domain. Methods We used comprehensive administrative register data from Denmark, comprising the full population and all COVID-19 tests, to estimate household transmission risk and attack rate. Results We studied the testing dynamics for COVID-19 and found that the day after receiving a positive test result within the household, 35% of potential secondary cases were tested and 13% of these were positive. After a primary case in 6,782 households, 82% of potential secondary cases were tested within 14 days, of which 17% tested positive as secondary cases, implying an attack rate of 17%. Among primary cases, those aged 0-24 were underrepresented when compared with the total population. We found an approximately linearly increasing relationship between attack rate and age. We investigated the transmission risk from primary cases by age, and found an increasing risk with age of primary cases for adults, while the risk seems to decrease with age for children. Conclusions Although there is an increasing attack rate and transmission risk of SARS-CoV-2 with age, children are also able to transmit SARS-CoV-2 within the household.